Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S2905 - S2922|
|Published online||02 March 2021|
Quadratic problems with two quadratic constraints: convex quadratic relaxation and strong lagrangian duality
Department of Mathematics, Statistics, and Physics, Qatar University, Doha, Qatar
2 Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
Accepted: 13 November 2020
In this paper, we study a nonconvex quadratic minimization problem with two quadratic constraints, one of which being convex. We introduce two convex quadratic relaxations (CQRs) and discuss cases, where the problem is equivalent to exactly one of the CQRs. Particularly, we show that the global optimal solution can be recovered from an optimal solution of the CQRs. Through this equivalence, we introduce new conditions under which the problem enjoys strong Lagrangian duality, generalizing the recent condition in the literature. Finally, under the new conditions, we present necessary and sufficient conditions for global optimality of the problem.
Mathematics Subject Classification: 90C20 / 90C22 / 90C26 / 90C42
Key words: Quadratically constrained quadratic programming / convex quadratic relaxation / strong duality / SDO-relaxation
© EDP Sciences, ROADEF, SMAI 2021
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